Given:
Consider the given statement is
[tex]\sqrt{\sec^2\theta+\text{cosec}^2\theta}=\tan \theta+\cot \theta[/tex]
To prove:
The given statement.
Solution:
We have,
[tex]\sqrt{\sec^2\theta+\text{cosec}^2\theta}=\tan \theta+\cot \theta[/tex]
Taking LHS, we get
[tex]LHS=\sqrt{\sec^2\theta+\text{cosec}^2\theta}[/tex]
[tex]LHS=\sqrt{\dfrac{1}{\cos^2\theta}+\dfrac{1}{\sin^2\theta}}[/tex]
[tex]LHS=\sqrt{\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta\cos^2\theta}}[/tex]
[tex]LHS=\sqrt{\dfrac{1}{\sin^2\theta\cos^2\theta}}[/tex] [tex][\because \sin^2\theta+\cos^2\theta=1][/tex]
[tex]LHS=\dfrac{1}{\sin\theta\cos\theta}[/tex]
[tex]LHS=\dfrac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}[/tex] [tex][\because \sin^2\theta+\cos^2\theta=1][/tex]
[tex]LHS=\dfrac{\sin^2\theta}{\sin\theta\cos\theta}+\dfrac{\cos^2\theta}{\sin\theta\cos\theta}[/tex]
[tex]LHS=\dfrac{\sin\theta}{\cos\theta}+\dfrac{\cos\theta}{\sin\theta}[/tex]
[tex]LHS=\tan \theta+\cot \theta[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
Write down the next two terms in this number pattern
2, 5, 9, 14, 20,0
Answer:
+3,+4,+5,+6,-20
Step-by-step explanation:
its:
2+3=5
5+4=9
9+5=14
14+6=20
20- 20=0
i believe so
The label on a 1.25 pound bag of wildflower seeds states that it will cover an area of 280 square feet. Based on this information, what is the number of square feet that 1 pound of wildflower seeds will cover?
Answer:
1 pound of sunflower seeds will cover about 187 square feet of land
Step-by-step explanation:
To solve this problem, we will have to assume that there is a linear relationship between the net weight of the wildflower seeds and the area of land it can cover when planted.
Based on this assumption, we can find the number of square feet that a 1 pound bag will cover, by setting up a simple relationship as shown below:
if 1.5 pounds covers 280 square feet
1 pound will cover x square feet.
by cross multiplying, we have that
x = (280 X 1) / 1.5 = 186.66 square feet.
Therefore, 1 pound of sunflower seeds will cover about 187 square feet of land
The triangle shown below are similar. Solve for x. 
Answer:
x=16
Step-by-step explanation:
27/45=(2x+7)/(4x+1)
cross multiply
27(4x+1)=45(2x+7)
108x+27=90x+315
108x-90x=315-27
18x=288
x=288/18
x=16
Looking at the image, The triangle shown below are similar. The value for x is 16.
What is the triangle about?Note that in the triangle given, the shapes are similar. Therefore:
27/45 = 2x + 7/ 4x + 1
3/5 = 2x + 7/ 4x + 1
So:
3 (4x + 1) = 5 (2x + 7)
12x + 3 = 10x + 35
12x - 10x = 35-3
2x = 32
x = 32/ 2
x = 16
Therefore, the value of x is 16.
Learn more about triangle from
https://brainly.com/question/17335144
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PLZ HELP MEEEEEEEEEEEEEEEEEE
On Robert’s shelf are 6 mystery books, 2 science fiction books, 3 adventure books, & 4 history books. Robert will randomly choose 1 book to read, not put it back and then grab another book to read. What is the probability that he chooses an adventure book and then a history book?
Answer:
2/35
Step-by-step explanation:
total of 15 books
P(Adv,Hist) = 3/15 · 4/14 = 1/5 · 2/7 = 2/35
Bryce and two of his friends went to eat at Texas Roadhouse. They split the bill evenly between them. Bryce share was $14.85. Write and solve an equation to find the total,t, of the bill .( please help asap and show all your work please)
As there are three people in total, the number of total shares is 3.
Let 1 share = x = $14.85
t = 3x
t = 3 (14.85)
= $44.55
Hope this helps!
help me please how do i do this
Answer:
41 degrees
Step-by-step explanation:
In a parallelogram, opposite angles are equal, so:
[tex]3x+11=5x-9\\-2x = -20\\x=10\\\\E = 3x + 11\\E = 3 * 10 + 11\\E = 30 + 11\\E = 41[/tex]
peter weighs 8kg heavier than Ailen.If 5/7 of Peter weight is 35kg,what is their total weight?
5/7 = 35 kg
1/7 = 7 kg
Peter weighs 49 kg
49 - 8 = 41 kg
Ailen weighs 41 kg
49 + 41 = 90kg
Their total weight is 90 kg
Lines De and AB are parallel.
D
C
E
B
А
Which angles represent alternate interior angles?
angles A and C
angles B and D
angles C, D, and E
angles B and C
Answer:
option 2
angles B and D are the alternate interior angles
lines DE and AB being parallel lines and and line BC being the transversal
Answer:
The answer is B and D
Step-by-step explanation:
Confirmed
What is the missing value of 5x-2y=30 (8,)
Answer:
In this equation, we can start by understanding that "x" has a value of 8, as given in the ordered pair. When multiplied by 5, this leads to "40 - 2y = 30". Next, we can subtract 40 from both sides of the equation. This leads us to a value of "-2y = -10". The next step would be to divide both sides by -2 as a way of isolating "y", which leads us to a final value of "y = 5". The final ordered pair would be (8,5).
Solve for x
[tex]\frac{x}{7}[/tex] − [tex]\frac{x}{9}[/tex] =−1
Answer:
[tex]x = \frac{ - 63}{2} \: or \: - 31.5[/tex]
Step-by-step explanation:
[tex] \frac{x}{7} - \frac{x}{9} = - 1[/tex]
Lets take the L.C.M of 7 & 9.
L.C.M of 7 & 9 = 63
[tex] = > \frac{9x - 7x}{63} = - 1[/tex]
[tex] = > \frac{2x}{ 63} = - 1[/tex]
Now lets multiply 63 on both the sides.
[tex] = > \frac{2x}{ 63} \times 63 = (- 1) \times 63[/tex]
[tex] = > 2x = - 63[/tex]
Now lets divide both the sides by 2.
[tex] = > \frac{2x}{2} = \frac{ - 63}{2} [/tex]
[tex] = > x = \frac{ - 63}{2} = - 31.5[/tex]
What is Ac Brainliest
Answer:
Ac is hypotenuse as c=90
Answer:
6
Step-by-step explanation:
let us call dc x
root(16+x2) =ac
root(25+x2)=bc
using the pytogoren theroum for traingle ABC we get
41+2x2=9 squared
41+2x2=81
2x2=40
x2=20
x=2 root 5
so then plugging the values in
you know ac=root(16+x2)
=root(36)
=6
We have 6 face red cards (JQK x 2) and 16 black cards, so a total of 22 cards.The red face cards and the black cards numbered 2-9 are put into a bag. Four cardsare drawn at random without replacement. Find the following probabilities:
a) All 4 cards are red
b) 2 cards are red and two cards are black
c) At least one of the red cards is red.
d) All four cards are black
Answer:
I dont know
Step-by-step explanation:
only doing it for points
Tia cut 4-meter 8-cenimeter wire into 10 equal pieces. Martha cut a 540-centimeter wire into 9 equal pieces. How much longer is one of Marta's wires than one of Tia's?
Answer: 19.2 cm
Step-by-step explanation:
A meter is equal to 100 centimetres so the total length of Tia's wire in centimetres is:
= 4.08 * 100
= 408 cm
She cuts this into 10 equal pieces:
= 408 / 10
= 40.8 cm
Martha cuts her 540 cm wire into 9 pieces. Each piece is:
= 540 / 9
= 60 cm each
The difference is:
= 60 - 40.8
= 19.2 cm
PLEASE HELP THIS IS DUE TODAY!!
Answer:
254 in
Step-by-step explanation:
1 yard = 36 in
7 yards = 36 (7)
7 yards = 252
add 2
254 in
:)
Answer: 254 inches
Step-by-step explanation:
1 yard= 36 inches x 7 (yards) + 2 inches= 254 inches
Cole buys a new laptop for $335. He makes a down payment of $50 and pays the rest in 6 equal monthly payments, p. What equation represents the relationship between the cost of the laptop and Cole’s payments?
Y=x(4)/2+3x(3)-2x-12
Answer:
[tex]\displaystyle y' = -2x^3 + 9x^2 - 2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = -\frac{x^4}{2} + 3x^3 - 2x - 12[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = -\frac{4x^{4 - 1}}{2} + 3 \cdot 3x^{3 - 1} - 1 \cdot 2x^{1 - 1}[/tex]Simplify Exponents: [tex]\displaystyle y' = -\frac{4x^3}{2} + 3 \cdot 3x^2 - 1 \cdot 2[/tex]Divide: [tex]\displaystyle y' = -2x^3 + 3 \cdot 3x^2 - 1 \cdot 2[/tex]Multiply: [tex]\displaystyle y' = -2x^3 + 9x^2 - 2[/tex]Solve the system by substitution.
y =
-4x
y = x - 5
Answer:
x=-1
Step-by-step explanation:
thanks I'm done pls
Answer: 1,-4
Step-by-step explanation: I noticed there are no steps for this one so I will go ahead and put them.
-4x+x=x-5+-x
combine:
-5x/5=-5/-5
x=1
Substitute:
y=-4x(1)
y=-4
so we get 1,-4
Finding which number supports the idea that the rational numbers are dense in the real numbers?
Answer:
an integer between –11 and –10
a whole number between 1 and 2
a terminating decimal between –3.14 and –3.15
Step-by-step explanation:
What is the slope of the line l ? (-2,9) (6,1)
The movie club is having a new member sale, so Mindy signs up. The equation -0.4x + 0.05y - 1.25 = 0 relates y, the total cost, and x, the number of months. What is the y-intercept of the line represented by the equation?
Answer:
Y intercept : ( 0 , 25 )
Step-by-step explanation:
Answer:
(0, 25)Step-by-step explanation:
We need to convert function to slope-intrcept form y=mx+b, where:
-0.4x + 0.05y - 1.25 = 0 {multiply both sides by 20}
-8x + y - 25 = 0 {add (8x+25) to both sides}
y = 8x + 25 ⇒ b = 25
Therefore y-intercept of the line is (0, 25)
6) Two boats set off from X at the same
time (below). Boat A sets off on a bearing of 325° and with a velocity of
14 km/h. Boat B sets off on a bearing of 2350 with a velocity of 18 km/h.
Calculate the distance between the boats after they have been travelling
for 2.5 hours. Give your answer to the nearest metre.
A
N
X Х
B
Answer:
The distance between the two boats after 2.5 hours is 57 m.
Step-by-step explanation:
The distance covered by each boat after 2.5 hours are:
speed = [tex]\frac{distance}{time}[/tex]
distance = speed x time
For boat A, speed = 14 km/h and time = 2.5 hrs.
So that,
distance = 14 x 2.5
= 35 km
For boat B, speed = 18 km/h and time = 2.5 hrs.
So that,
distance = 18 x 2.5
= 45 km
The distance between the two boats after travelling 2.5 hours can be determined by applying the cosine rule. Let the distance be represented by x, so that:
[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] - 2bc Cos A
[tex]x^{2}[/tex] = [tex]45^{2}[/tex] + [tex]35^{2}[/tex] - 2(45 x 35) Cos [tex]90^{o}[/tex]
= 2025 + 1225 - 3150 (0)
= 3250
x = [tex]\sqrt{3250}[/tex]
= 57.0088
x = 57.0 m
The distance between the two boats after 2.5 hours is 57 m.
I’m confused on my math someone help
Okay so we’re trying to find out if they are true or false I guess so the first question is HELP MEEE
Answer:
False, True, True are thr answers
Find the expression that represents the sum of 2i3+5i2-6i and 2i2-3i+8.
Dry-by-step explanation:
Kznyuszc kubysadnuailsdaieubvaeryulbvaulybeffn
Ioaer
PLz help I will give brainliest!!!!! and extra points
Hey there!
The answer to your question is [tex]95.55[/tex]
Formulas:
Area of semi-circle = [tex]\frac{1}{2}(\pi r^2)[/tex]
Area of rectangle = [tex]lw[/tex]
Area of triangle = [tex]\frac{bh}{2}[/tex]
Now solve:
semi-circle
[tex]\frac{1}{2}\pi3^2[/tex]
[tex]\frac{1}{2}\pi9[/tex]
[tex]4.5\pi[/tex]
(We will use 3.14 as approx. for pi)
[tex]4.5 * 3.14\\23.55[/tex]
rectangle
[tex]10(6)\\60[/tex]
triangle
[tex]\frac{4(6)}{2}[/tex]
[tex]\frac{24}{2} \\12[/tex]
Now add them all together:
[tex]23.55+60+12\\95.55[/tex]
Have a terrificly amazing day!
HELP ASAP 10) Determine the volume; just answer without the units
B
9.5 in.
3.75 in.
8 in.
Answer:
Volume is 285
Step-by-step explanation:
We start by calculating the area of the base
Mathematically, we have a rectangle as the base
So, the area of the base will be;
3.75 * 8 = 30
We now multiply this by the height to get the volume
we have this as:
30 * 9.5 = 285
26
24
10
HELP PLSSsSs
Answer:
what is the question? all I see is a drawing w labels
Prove that
cos 9°+sin 9°/cos9°-sin9° =cot 36°
plzz fasstttt i need to writw this!!!!!!!!!
Answer:
Step-by-step explanation:
LHS = (Cos9° + Sin9°) / (Cos9° - Sin9°)
Divide by Numerator and Denominator by Cos9°
LHS = (1 + Tan9°) / (1 - Tan9°)
= (Tan 45° + Tan 9°) / (1 - Tan 45° * Tan 9°)
= Tan (45°+9°)
= Tan 54°
= Cot 36°
hope it helps :)
Factoriza el siguiente trinomio 6x^2 – 26x – 200
Answer:
2 (x + 4)(3x - 25)
Step-by-step explanation:
[tex]6 {x}^{2} - 26x - 200[/tex]
[tex]3 {x}^{2} - 13x - 100[/tex]
[tex]2 (x + 4)(3x - 25)[/tex]
Find the missing length of the triangle.
A = 3.4 cm
C = 1.6 cm
B = ?
Answer: b = 3
Step-by-step explanation:
1. a^2 + b^2 = c^2
2. 1.6^2 + b^2 = 3.4^2
3. 2.56 + b^2 = 11.56
4. 11.56-2.56 = b^2
5. 9 = b^2
6. 3 = b